Question 249908
Using long division:
<pre>
        3x^2  - 1x    +  4
        ________________________
2x - 3 /6x^3  -11x^2  + 11x  - 2
        6x^3  - 9x^2   <==== Subtract
        ------------
              -2x^2   + 11x
              -2x^2   +  3x    <==== Subtract
              -------------------
                         8x  - 2
                         8x  -12   <==== Subtract
                         -------
                              10
</pre>
So {{{(6x^3 - 11x^2 + 11x - 2)/(2x - 3) = 3x^2 - x + 4 + 10/(2x - 3)}}}